MathLabs

Problem 5

Find the greatest integer nn for which there are n+4n+4 points A,B,C,D,X1,…,XnA,B,C,D,X_1,\dots,X_n in the plane with AB≠CDAB\ne CD such that, for each i=1,2,…,ni=1,2,\dots,n, triangles ABXiABX_i and CDXiCDX_i are congruent.
Step 2 of 6: Get the first bound
Previous stepNext step
Xi∈(ΓA∪ΓB)∩(ΔC∪ΔD).X_i\in(\Gamma_A\cup\Gamma_B)\cap(\Delta_C\cup\Delta_D).
Detailed analysis

There are four pairs of circles. Each pair has at most two intersection points, so at most eight points can satisfy the necessary side-length conditions.